A coordinate measuring machine includes a support structure, an articulated arm having a first end pivotally connected to the support structure and a second end that is movable in a horizontal plane. A Z-ram assembly is mounted to the second end of the articulated arm. The Z-ram assembly includes a Z-ram housing and a probe that is vertically movable with respect to the Z-ram housing. The probe is movable within a measurement volume defined by the articulated arm and the Z-ram assembly. The coordinate measuring machine further includes a measuring assembly for determining coordinates of the probe in the measurement volume. The articulated arm preferably includes first and second arm assemblies that have a parallelogram configuration to prevent substantial rotation of the Z-ram assembly as the articulated arm is moved in the horizontal plane. The angles of the articulated arm are preferably measured using a sensor which includes a pattern of parallel, straight grating lines.